Corollary.

If fff satisfies the conditions of the theorem, then for all x>1x1x>1, ∑n≤xf⁢(n)=O⁢(xlog⁡x⁢∑n≤xf⁢(n)n)subscriptnxfnOxxsubscriptnxfnn\displaystyle\sum_{{n\leq x}}f(n)=O\left(\frac{x}{\log x}\sum_{{n\leq x}}\frac%
{f(n)}{n}\right).